Let a function f E C[-1, 1], changes its monotonisity at the finite collection Y ：= {y1,……, ys} of s points Yi ∈ （-1, 1）. For each n 〉 N（Y）, we construct an algebraic polynomial Pn, of degree 〈 n, which is c...Let a function f E C[-1, 1], changes its monotonisity at the finite collection Y ：= {y1,……, ys} of s points Yi ∈ （-1, 1）. For each n 〉 N（Y）, we construct an algebraic polynomial Pn, of degree 〈 n, which is comonotone with f, that is changes its monotonisity at the same points yi as f, and ｜f（x） - Pn（x）｜ ≤ c（s）ω2 （f1 √1-x^2/n）,x∈ [-1,1] where N（Y） is a constant depending only on Y, c（s） is a constant depending only on s and ω2 （f, t） is the second modulus of smoothness of f.展开更多
The large time behavior of solutions to the two-dimensional perturbed Hasegawa- Mima equation with large initial data is studied in this paper. Based on the time-frequency decomposition and the method of Green functio...The large time behavior of solutions to the two-dimensional perturbed Hasegawa- Mima equation with large initial data is studied in this paper. Based on the time-frequency decomposition and the method of Green function, we not only obtain the optimal decay rate but also establish the pointwise estimate of global classical solutions.展开更多
In this paper we focus on the initial value problem of a hyperbolic-elliptic coupled system in multi-dimensional space of a radiating gas. By using the method of Green function combined with Fourier analysis, we obtai...In this paper we focus on the initial value problem of a hyperbolic-elliptic coupled system in multi-dimensional space of a radiating gas. By using the method of Green function combined with Fourier analysis, we obtain the pointwise decay estimates of solutions to the problem.展开更多
The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence ...The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.展开更多
文摘Let a function f E C[-1, 1], changes its monotonisity at the finite collection Y ：= {y1,……, ys} of s points Yi ∈ （-1, 1）. For each n 〉 N（Y）, we construct an algebraic polynomial Pn, of degree 〈 n, which is comonotone with f, that is changes its monotonisity at the same points yi as f, and ｜f（x） - Pn（x）｜ ≤ c（s）ω2 （f1 √1-x^2/n）,x∈ [-1,1] where N（Y） is a constant depending only on Y, c（s） is a constant depending only on s and ω2 （f, t） is the second modulus of smoothness of f.
基金supported by the National Natural Science Foundation of China(11231006)
文摘The large time behavior of solutions to the two-dimensional perturbed Hasegawa- Mima equation with large initial data is studied in this paper. Based on the time-frequency decomposition and the method of Green function, we not only obtain the optimal decay rate but also establish the pointwise estimate of global classical solutions.
文摘In this paper we focus on the initial value problem of a hyperbolic-elliptic coupled system in multi-dimensional space of a radiating gas. By using the method of Green function combined with Fourier analysis, we obtain the pointwise decay estimates of solutions to the problem.
基金supported by the National Natural Science Foundation of China(11271141)Chongqing Science&Technology Commission(cstc2018jcyjAX0787)
文摘The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.
